mp4 to h263 conversion is typically related to attempts to change the encoding of the video track from within the MP4 container, in this case probably from H.264 to H.263. This is done so videos can be played back on devices that do not support h.264 codec, such as old TVs.
Various video editors (like FFmpeg) and encoding tools are your best choice, but the same applies to various multimedia converters that allow you to change encoding of the video track, not just different container.
Updated: September 20, 2023